The Prime Minister said he is open to “all ideas and proposals” that would allow people to own the bank in a “genuine way”.

A mass share distribution to the public would be the biggest such exercise undertaken in the UK since the utilities sales in the 1980s.

Speaking to reporters in New York the Prime Minister was asked if there are “any circumstances” in which RBS could be sold back to the private sector at a loss to the taxpayer.

He refused to rule it out and said: “On RBS I think the important thing is to return this bank to health, and there’s a strategy underway, it’s made some progress on selling down surplus assets and building up positive assets.

“And I keep a very close eye on this and want to make sure progress is made as fast as possible. In terms of returning RBS to the private sector involving people in owning this bank in a genuine way, I’m open to all ideas and proposals.”

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George Osborne, the Chancellor, is said to be in favour of a public sell-off because it would give the British people a direct stake in any future recovery of RBS, giving him room for manoeuvre if he decides to sell the bank stake at a price below that paid by the Labour government in 2008.

Many City observers remain sceptical about an early sell-off, pointing out that RBS share are trading at just over £3 each, compared to the £5 paid by the last Labour government.

A sale at this price would translate into a loss to the taxpayer of about £20 billion.

Analysts believe the share price would have to rise above at least £4 to make the sale politically respectable.

The Prime Minister added: “But it seems to me the primary question is getting this bank back into good health, and then obviously… there are connections between the ownership and health but step one is to continue the path to health and step two is to think about ways of changing its ownership.”

It is the first time the Prime Minister has publicly acknowledged the possibility of a sell-off at a loss to the taxpayer.

Some Treasury figures believe that a “Tell Sid” privatisation, similar to the 1980s British Gas sell-off, would be the quickest and most effective way for the state to shed its shares in RBS as well as Lloyds Banking Group.

Mr Osborne is keen to begin the privatisation of RBS before the election, to demonstrate that the banking crisis is finally passing.